package A;

sub new {
    my ( $class, $href ) = @_;
    my $self = { dbi => $$href{dbi} };
    $self->{helper} =
        Helper->new( helper_function => sub {
                      my $dbi = $$href{dbi};
                     return  $self->this_is_from_A($dbi, @_);      # pass $dbi
            } );
    bless $self, $class;
}

sub do_something {
    my $self = shift;
    $self->{helper}->called_from_helper();
}

sub this_is_from_A {
    my ($self, $dbi, $arg) = @_;                                   # receive $dbi
    print "$arg\nthis_is_from_A using $dbi\n";
}